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Generating all circular shifts by context-free grammars in Chomsky normal form
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In this article, a few families of context-free grammars were investigated with respect to their descriptional complexity, i.e., the number of nonterminal symbols and rules π(n) of a given grammar as functions of n. These ν and π happen to be functions bounded by low-degree polynomials.Abstract:
Let {a1, a2,..., an} be an alphabet of n symbols and let Cn be the language of circular or cyclic shifts of the word a1a2 ... an; so Cn = {a1a2 ... an-1an, a2a3 ... ana1, ..., ana1..., an-2an-1}. We discuss a few families of context-free grammars Gn (n ≥ 1) in Chomsky normal form such that Gn generates Cn. The grammars in these families are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols ν(n) and the number of rules π(n) of Gn as functions of n. These ν and π happen to be functions bounded by low-degree polynomials, particularly when we focus our attention to unambiguous grammars. Finally, we introduce a family of minimal unambiguous grammars for which ν and π are linear.read more
Citations
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Generating all permutations by context-free grammars in Chomsky normal form
TL;DR: In this paper, the authors consider context-free grammars in the normal form that generate a finite language of all n! strings that are permutations of n different symbols (n ≥ 1).
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Lower bounds for context-free grammars
TL;DR: Ellul, Krawetz, Shallit and Wang prove an exponential lower bound on the size of any context-free grammar generating the language of all permutations over some alphabet, and obtain exponential lower bounds for many other languages.
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Permuting operations on strings and their relation to prime numbers
TL;DR: The structure and the order of the cyclic group generated by X"n"n, an integer n X-prime, is investigated and some properties of these X-primes are shown, particularly, how they are related to X^'-primes as well as to ordinary prime numbers.
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Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form
TL;DR: This work studies a few families of context-free grammars $G_n$ ($n\geq1$) in Greibach normal form such that G_n generates $C_n$.
Journal ArticleDOI
Generating all permutations by context-free grammars in Greibach normal form
TL;DR: In this article, context-free grammars G"n in Greibach normal form were investigated with respect to their descriptional complexity, i.e., they determine the number of nonterminal symbols and their production rules as functions of n.
References
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Book
Introduction to formal language theory
TL;DR: This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.
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Some classifications of context-free languages
TL;DR: In this paper some other classifications of grammars and languages are investigated, chosen in such a way as to characterize some aspects of the intuitive notion about complexity (of the description of the description) of gramMars and Languages and their intrinsic structure.
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Concise description of finite languages
TL;DR: It is shown that if the limit of certain sequences of finite languages is of type X1 then the type X complexity of each of the finite languages involved must be low.
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Complexity of normal form grammars
TL;DR: Greibach normal form Grammars and position restricted grammars will be investigated from the point of view of descriptional complexity of context-free languages.